Yes. Many motherboards will not function correctly without the ATX12 connector plugged in - coincidentally, a mistake I made this past week, since I didn't see the connector on a system I was building.

And the system didn't boot until I plugged the connector in.
Now, I have seen 4pin molex to ATX12 adapters at computer shows, so you can use a power supply that doesn't have an ATX12 plug.. I'm trying to locate one now. When I find it, I'll post a link.
Edit: Okay -
HERE is a place that has the connector you'd need.
Drive to P4 Adapter
Converts single drive connector to P4 connector. Allows for non-P4 ATX power supply to support P4 motherboard. Space saving design.
Availability: Usually ships the same business day
drive-to-p4-adapter price: $5